1. Field of the Invention
The present invention relates to reconstruction of sampled signals. More particularly, the invention relates to a system and method for characterizing a compressed sensing system so that the compressed sensing system may more accurately reconstruct a sampled signal.
2. Description of the Related Art
Sampling is a method of converting an analog signal into a numeric sequence. Analog signals are often sampled at spaced time intervals to form digital representations for storage, analysis, processing, or other uses. Typically an analog signal must be sampled at or above its Nyquist rate, which may be defined as twice the bandwidth of the analog signal or twice the highest frequency component of the analog signal in the case of baseband sampling. For wide bandwidth signals, sampling at the Nyquist rate requires a great amount of computing resources, processing power, and data storage. Furthermore, if the sampled data is to be transmitted to a secondary location, a large amount of bandwidth is required as well.
Compressed sensing is one technique developed to address high sampling rates, computing resources, processing power and data storage problems of traditional signal processing techniques. Unfortunately, compressed sensing techniques are highly dependent on the compressed sensing matrix utilized by the compressed sensing apparatus. Utilizing a random compressed sensing matrix which possess certain required properties have been shown to be able to reproduce a signal when used with a compressed sensing apparatus. Unfortunately, while utilizing a random matrix may be effective it should be possible to better reconstruct signals. The first step in doing so, is to understanding the input/output relationship of compressed sensing apparatus so that it can be optimized. No method for doing so has been developed.
Accordingly, there is a need for a system and method for accurately characterizing a compressed sensing apparatus.